Inertial concept for cable dynamics



Sept. 8, 1970 M. A. NATION 35527044 INERTIAL CONCEPT FOR CABLE DYNAMICS K n Filed May 2o, 196e United States Patent O 3,527,044 INERTIAL CONCEPT FOR CABLE DYNAMICS Milton A. Nation, 905 Moraga Drive, Los Angeles, Calif. 90049 Filed May 20, 1968, Ser. No. 730,681 Int. Cl. D02g 3/02; C22c 15/00 U.S. Cl. 57-139 4 Claims ABSTRACT OF THE DISCLOSURE This invention relates generally to an inertial concept for the dual purpose of minimizing inertial forces and sustaining inertial effects for protracted periods in dynamics of wire and cable systems when exposed to either normal or severe environments.

Titanium and titanium metal alloys have some special mechanical properties which uniquely satisfy a broad range of inertial parameters; this makes up for the relatively high price, and the difficulties experienced in processing rutile and ilmentite ores into titanium sponge followed by conversion into cable and monolament tension members. Other refractory metals have these properties but their suitability is more specialized and limited.

Price indices for processing all structural forms of titanium have been substantially reduced through a relatively short history of processing and they continue on a downward trend while processing improves. Titanium cable is being produced in quantity for one oceanographic application that quite fully embodies the inertial concept. This example is on a favorable cost-effective basis due to the advantages of the inertial concept.

For four previous years, as will be evident from application Nos. 495,312 and 495,313, titanium wire has been fabricated and cable designed to demonstrate the effectiveness of these titanium components in these dynamic modes of cable systems, (l) tension, (2) motion and (3) viscous drag. Research work has been performed in order to make titanium wire and cable technology feasible, and further, to reduce it to practise. Hardware produced includes general purpose cable for multipart reeving systems used i-n motion such as cranes, elevators and mining rigs, aircraft control cables that receive low order impacts in tension and bend loading from autopilot coupling, air-sea rescue cable in tension, motion and drag, airborne cargo handling requires composite cable for use in all modes, and monofilament and cable for deep ocean moorings and balloon tethers primarily used in the tension mode.

Special electrical cores, fittings and joints have been attendantly developed which have thus involved the use of novel supporting fabrication techniques.

Principal special properties are corrosive inertness in air and seawater, moduli of elasticity that are effective in resisting inertial loading and impacts, the highest strength-to-weight ratio of all commonly used metals to result in major weight savings, and a high damping index that moderates vibration in shock environments.

Other significant properties found in the development of titanium and inertial technologies are: (a) unusual linear loading to the proportional limit, (b) low gap between yield and ultimate strengths, (c) limited loss of 3,527,044 Patented Sept. 8, 1970 "ice strength and a marked degree of cyclic linearity when titanium cable sustains bending motion, and (d) relatively high internal damping when titanium wire is in the work-hardened condition and at seawater temperatures.

rIhese properties are all favorable to dominance of inertial characteristics, resulting in specifically unique passive inertness, high loading limits, protracted cycle life, and further, they are conductive to special processing.

It may now be apparent that titanium wire and cable is suitable and may be introduced for use in commercial and military systems on a gradually improving costeffective basis. These components have been found especially effective in developing high-performance rates while passive to severe aerospace and hydrospace environments. For this reason titanium tension members are characterized in outline, and compared to steel members as the standard, to show the basic advance which may be achieved by use of these technologies. An illustrative comparison of load dellection characteristics is shown in FIG. 1.

Strength and tension advantages- (1) High strength to weight ratios combined with a high percentage of the breaking strength and low gap between yield and ultimate strengths. Tensile strength range approximates the range of structural steel wire. The `density comparison between titanium and steel is .163 vs. .290 lb. per cu. in., or 4 to 7 ratio.

(2) High usable strength together with linear load deflection for improving cable designs, etliciency and coupling to other systems.

(3) High energy storage during stress-propagation and low reaction to speed changes and longitudinal and transverse impacts or high impact tolerance in the shock environment.

(4) High prestressing limit based upon load linearity to the proportional limit for effective post-processing.

Elasticity, bending and stiifness advantages- (5) Greater flexibility due to lower moduli reduces motion and handling inertia.

(6) Lower bend stresses decreases loss of cable strength and internal moments of inertia in bending motion and reduces fatigue rate.

(7) Lower elastic and frictional stiffnes reduces energy required to pay out and retrieve cable.

(8) Increased cable efliciency and flexibility for a specified diameter reduces number of wires, and smaller diameter cable may be used.

Inertial advantages- (9) Prevents rapid degradation due to corrosive inertness.

10) Reduces forces of inertia due to density, strength, and elastic advantages.

(1l) Reduces wear and fatigue based upon moderated stresses in dynamic states so that these effects become balanced when stresses are controllable.

(12) Increases cycle life through this balance together with the use of solid films.

Performance advantages- (13) Dynamic margins under protracted cycle life and passively inert conditions may be closely tailored for level output, and low dynamic factors of safety may be assigned.

(14) Linearized cyclic conditions contribute markedly to protracted and reliable serviceability.

(15) Decrease in motion acceleration and deceleration inertias, with lower impacts, results in more even inertial force levels, and permits increased handling rates.

(16) Decrease in work required to move and bend cable with loads also contributes to the increase in handling rates.

(17) Strand construction may be optimized and cable diameters minimized on the basis of lower forces and effects of inertia, and for making coupled system improvements.

Notes: (1) Performance merit is marked; in a minesweeping application weight is reduced from 25 pounds per 100 feet to 6 pounds per 100 feet of cable, a gain of 400% in terms of weight and thus drag forces are of a lower order. For helicopter sweeping, weight savings and drag is uniquely beneficial. (2) A technique may now be seen as necessary for synthesizing these advantages and tailoring close margins for each dynamic mode and high performance application.

It may be convenient and desirable at this point to define technical terms as used.

Inertial concept is the embodiment of physical principles of elastic cable systems into performance characteristics to more efficiently perform work, and accomplish time-varying interchange of kinetic and elastic energy that occurs with coupled systems, by the control and measurement of inertial forces and effects. In so doing, inertial characteristics are embodied uniquely in two parts, one combining activated, inertial, elastic and frictional elements to perform work, and another combining passive inductive, capacitive and resistive elements to sustain inertial forces and effects for protracted periods.

Massive strength approach is the established practice of buttressing loading with massive strength, accompanied by limited elasticity and high stiffness, because of severe limitations on load capacity and high safety factors due to relatively rapid deterioration of performance characteristics from fatigue and corrosion.

Inertial effects are the passive results of dynamic states and active wok in sustaining primary, inertial, and impact loading to cause corrosion, fatigue, and wear.

Active describes the physical nature of inertial characteristics when applied to inertial forces.

Passive describes the physical nature of inertial characteristics caused by the slow, cumulative effects of the interchange and absorption of kinetic and elastic energy. The common electrical analogy used for inertial elements is applied on a mechanical basis.

Dominant relates to controlling physically and characteristically overbalancing, or is a prevailing influence in cable dynamics.

Moderate to reduce in the inertial sense so as to normally change from severe to mild, or from dominant to well controlled.

New cable technology comprises novel cable principles, appropriate fabrication procedures, and new features embodied in processing and production as generally combined in titanium and inertial technologies and miscellaneous innovations.

Suitability applies primarily to the material requirements for inertial properties of wire and characteristics of cable in the fulfillment of this concept especially embracing performance, dynamics, environment, conversion, fabrication and processing.

Technical synthesis the methodology of developing and combining inertial properties and characteristics into performance effectiveness.

Power of synthesis is effective integration and cumulation of dynamic and inertial parameters embodied in performance characteristics; power is achieved by materials selection, unitizing components, inertia control, use of design criteria and parameters, and fabrication and processing techniques.

Wear is used to mean a progressive wearing away of contacting surfaces so that the phenomenons of wear and fretting fatigue are combined, whereas, corrosion fatigue is treated separately, not normally including stress corrosion since it has not been found in small wire.

Linearity an inertial mechanical property for describing either cable loading or cyclic characteristics depicted in geometrical plotting; it indicates the part of the plot which forms a straight line to show essential linearity as differentiated from the part which deviates to become nonlinear or curvalinear. The loading point in titanium wire at which plastic flow is initiated normally becomes non-linear with heavier loading until a critical state of mass is reached.

Tailor a design practice to embody inertial characteristics in dynamic modes of cable to provide effectively the (l) stranding arrangement, and (2) loal inertial factors of safety.

Stratification of stresses is a technique which tends to separate stresses between cores and outer strands, or in contrahelical layers, to prevent overstressing of cores, and as feasible, dominantly control this separation, rather than to permit stresses to combine so that their effects in large part remain indeterminant.

Nomenclature frequently used is:

Azcross-section area, sq. in. E=modulus of elasticity Ec=modulus of cable elasticity ln=masls density of material, lbs. per sec.2/ft.4 pc=mass density of cable, lbs. per sec.2/ft.1 Fzforce in ft./lbs.

T=tension, lbs.

q=cross section area of cable, sq. ft. ry=T/Q=stress, p.s.f.

at=tensile stress, p.s.f.

abzbend stress, p.s.f.

ec=surface contact stress ai=impact stress, p.s.f.

a=wire diameter, sq. in.

D=cable diameter, sq. in.

t=time, sec.

c=longitudinal wave velocity, f.p.s. E=transverse wave velocity, f.p.s. V0=impact velocity, f.p.s. Pi=internal pressure, p.s.f. m=weight, lbs. per cu. in. u=displacement from equilibrium f=frequency, c.p.s.

g=gravity, 32.2 ft./sec.

wi=weight, lbs.

lzlength, ft.

The distinct contrast between this concept as defined and reduced to practice, and the massive strength approach may now be shown. Work is performed and energy interchanged efficiently by simply combining inertially suitable wire properties and cable characteristics to obtain protracted high performance output when inert to the rigors of the environments now growing in use. It is also evident that existing cable technologly, with conventions and constraints for which standards have long been defined, such as by the American Petroleum Institute for oil well rigs, may now be largely replaced by this novel concept which requires broad use of all parameters of inertial significance. To fully exploit performance gains, in lieu of constraints such as the capacity limitation of twenty percent (20%) of the minimum breaking strength imposed during oil well rig operations, it may be replaced in all three dynamic modes.

A deep ocean mooring, for example, as a specific high performance application in the tension mode, need only embody tension parameters, largely eliminating bending parameters while minimum diameter is of critical importance so as to minimize mass and hydrodynamic drag.

Thus first order attention is given to inertial characteristics with next attention to simple stranding design and high cable efficiency; diameter is also critical in its relation to the effect of tautness upon strumming By marked contrast in steel oceanographic cable first attention must be given to a low primary load limit with a high static factor of safety; and it may be found necessary to use diameter steps in such a mooring to prevent the cable fracturing of its own weight. A larger diameter cable is required first because of necessary massiveness and grossness in parameters and next because of dangerously high tension peaks. Cable strength must be high to buttress against loss of strength and stiffening due to corrosion. It is also clear that massive strength is a temporizing expedient in the salt-water environment so that replacement of the mooring must be anticipated after a year when reliability becomes uncertain.

A number of objects of the present invention are now evident and are accordingly set forth:

(l) Well defined performance characteristics are embodied in cable systems by effective combinations of inertial, elastic and frictional elements for the purpose of performing work at markedly higher efficiency than is characteristic of massively coupled systems.

(2) Well defined passive characteristics are embodied to accomplish interchange of kinetic and elastic energy by effective combinations of inductive, capacitive and resistive elements for sustaining inertial effects for protracted periods in normal environments including aerospace and hydrospace.

(3) Moderate two elemental tension stresses, axial and transverse, and associated compressive stresses by reduction of characteristic primary, inertial and impact loading, and use of other new cable technology.

(4) Stratify two elemental tension stresses, axial and transverse and associated compressive stresses, between core, layers and outer strands Iby using lower moduli wire in cores and core strands, preparing layer interfaces for low sliding friction and bearing loads, and use of new cable technology to avoid core overstressing and effectively sustain continuous low order impacts such as strumming or self excited vibration.

(5 Halve impact stresses in shock environments including low order vibratory impacts compared to these stresses characteristic of steel cable because of lower mass density and higher cable elasticity.

(6) Increase lay lengths of strands and layered cable compared to commonly used lay lengths because of greater elasticity to further reduce compressive and torsional stresses, increase breaking strength, and reduce constructional stretch to result in substantial dynamic improvement especially including greater stratified dominance.

(7) Increase the function of cores and decrease the function of outer strands in all three dynamic modes, except when composite cable is required for other than dynamic characteristics, by increasing performance characteristics of the core to dominantly perform work in rela tion to outer strands, while on the other hand, outer strands may be used to dominantly sustain bending motion in cable dynamics primarily when the motion mode is characteristic of the system.

(8) Obtain linear cycling performance so as to achieve protracted service by controlling two dynamic conditions, (l) fatiguing hyperbolic condition at high levels of loading, and (2) fatiguing parabolic condition in severe bending motion by use of simple and appropriate design criteria in systems.

(9) Provide lubrication, more or less permanent and stable to minimize and control sliding friction and frictional stiffness by use of suitable solid films on wire surfaces corrosively inert in air and water,

(10) Achieve a practical balance between the inertial effects of wear and fatigue by (l) obviating corrosive degradation, (2) use of solid film lubricants, (3) stress moderation, and (4) control of tension and bending dynamics.

(11) A corollary object to moderating dynamic conditions and stresses while balancing wear and fatigue is to essentially eliminate severe effects of dominant stresses as these manifest themselves to include cable crushing, early broken wires, and markedly reduced performance levels and service life.

(12) Minimize cable diameter below conventional diameters to improve performance primarily by reducing mass more than one-half and increasing usable strength.

(13) Maximize damping in fluid flow in the drag mode because of the characteristically high damping index of titanium, and by workhardening this wire for use in the sea water temperature range, and also appropriately unitizing high damping low modulus materials used in the electrical core.

(14) Design cable with flexibility suitable for high rate handling speeds to couple with driving and accumulation components, when used in motion and drag, and synthesize lower mass, lower frictional stiffness, and probably, shorter tow lengths for cumulative system gain.

(l5) Fabricate, process and condition electrical conductor wire so it may be inertially unitized or integrated to augment and sustain performance of mechanical components rather than to compromise it.

(16) Synthesize inertial gains by use of a methodology so as to exploit the power of synthesis in developing maximum dual inertial characteristics.

In accordance with the duality of inertial characteristics in the present invention, basic consideration is first given to the efficient use of inertial forces and the embodiment of active characteristics to perform work, with next consideration to passive characteristics developed in stranding design suitable for sustaining inertial effects of the application, the design being simplified compared to steel cable used in the same application.

Four research areas have been pursued, after developing two titanium wire characters, to reduce inertial technology to practise:

(l) Solid film lubrication has been developed for use with titanium-base and steel structural wire for the purpose of increasing cycle life, but more directly, to achieve a passive balance between fatigue and wear.

(2) The role of cores in cable dynamics has been increased in function and efficiency, primarily the tension function including avoiding over-stressing, and to resist continuous dynamics of the shock environment; in this role vibratory conditions are more effectively sustained.

(3) Composite cable with electrical cores has been developed to rst sustain dynamics without compromising inertial integrity of the mechanical components, and next to augment as feasible the dual inertial characteristics; of course, the primary electrical function of the core must not be materially compromised, but this research has been found to avoid, in Several cases, detrimental compromise while otherwise improving cores.

(4) Correlation of cyclic results between the two elemental tension conditions in cable dynamics, hyperbolic and parabolic, has shown that these two distinctly different curvalinear effects, may be combined to achieve a major linear increase in cycle life. In so doing there are test data and indications that typical dominance of stresses which has in the past severely limited cycle life, may in fact be controlled for practical purposes.

Novel features of this invention are set forth with particularity in the appended claims. The invention as to organization, technical and physical synthesis, and operation, together with other advantages and objects, will best be understood from the following description.

Two wire characters have been developed for use in high performance applications so as to have suitable properties for use in (l) the tension mode, this especially requiring uniaxial strength with high elasticity to result in low impact stresses, and (2) for bending motion, this requiring high fracture toughness and fatigue strength with high elasticity. Ti-13V-11Cr-3Al has proven most suitable in the first mode, and Ti-6Al-4V in the latter. Ti-13V- 11Cr-3Al has also proven to be most formable, an important attribute when the feasibility of the development of suitable mechanical properties was being investigated and tested, and the conventional difficulties found in wiredrawing proved to be greater with titanium than steel. It is of course practical to fabricate titanium structural wire under normal conditions with conventional equipment except that stage annealing should be performed in a vacuum or under inert conditions.

Mechanical properties of both titanium structural wire characters as these translate directly into inertial characteristics are itemized:

(a) Average tensile strength, cold worked-230,000 to 240,000 p.s.i., Ti-13V-11Cr-3Al. 190,000 to 200,000 p.s.i., Ti-6Al-4V (b) Average tensile strength, plus aged- 270,000 to 280,000 p.s.i., Ti-l3V-11Cr-3Al; 210,000 to 220,000, Ti- 6Al-4V (c) Modulus of elasticity, Ti-l3V-11Cr-3Al-14-5 106 (d) Modulus of elasticity, 'I`i-6Al-4V---l6.5 l0(i (e) Elongation--35%; depends upon workhardenmg (f) Torsions-greater than `65% mild plow steel- 150% after density factor applied.

(g) Density-.160# per cu. in. (commercially pure) (h) Creep-not found in cable applications (i) Permanently non-magnetic (j) Stress corrosionphenomenon not yet found in wire (k) Inert to impingement attacks of sea water salts Titanium wire, after novel processing, in both wire characters has been stranded and closed into cable as large as 3A" diameter at top machine speed using special techniques. In addition to Ti-6Al-4V, another alpha-beta alloy Ti-6Al6V2Sn has been fabricated into Wire on a test basis; other all-beta alloys in addition to Ti-13V11Cr- 3Al also indicate promise in further developing wire technology.

Property and processing data for other structural forms of titanium and non-ferrous metals has been primarily obtained from Defense Metals Information Center (DMIC), at Battelle Memorial Institute and from Aerospace Structural Metals Handbook prepared for Air Force Materials Laboratory, Wright-Patterson Air Force Base.

Load deflection comparison of three cables of identical construction, 1/4" 7 x 7, fabricated from high grade stainless steel, Ti-l3V-11Cr-3Al and Ti-6Al-4V illustrates single cycle performance in loading to the point a critical state of mass or fracture occurs. Characteristics of these cabes are noted:

(1) Linearity is high approximating 94% for Ti13V 11Cr-3Al, and 80% for Ti-6Al-4V compared to 57% for steel.

(2) Breaking strength is slightly higher for Ti-13V- 11Cr-3Al compared to stainless steel which then results in a doubling effect of strength Weight ratio.

(3) Linear loading approximates 50% more for Tito stainless steel.

(4) Capacity for energy storage and absorption substantially increases in that a doubling effect is approached by Ti-6Al-4V and about a sixty percent (60%) increase for Ti-13V-11Cr-3Al.

(5) Wire sizes are identical for all three cables as follows: core strand .032 and .0305" and outer strands .0285 and .027".

The composite diagram, FIG. l, is based upon tests for which there are separate diagrams, so that a transposition has been made which loses some accuracy that has been contributed to by slight variation in specimen length. In composite form however a comparison of loading linearity, and capacity to absorb energy and perform work is clearly seen.

Frictional and elastic stiffness is minimized dynamic and inertial gains. lt may now be pointed out that the work performed in test bending a free ft. (3') specimen, 6 x 19 lubricated steel cable, to 180 measured 14 lbs., while the same length titanium specimen, 6 x 19, lubricated with solid film measured 5 lbs.

FIG. 1 shows load deflection diagrams of two 1A 7 x 7 Ti-6Al-4V specimens used in tests. This same cable was used in the test which was continued for fourteen (14) days to 1,000,000 cycles (2 million reversals) with a load deflection diagram being taken at the conclusion of this test, FIG. 1a, at which time no measurable wear was found. These results show both low elastic and frictional stiffness, with residual solid film lubricant present, and a condition of higher work hardening but no loss of strength.

The effects of reduced stiffness result in extremely ilexible cable and low energy required to wrap it around sheaves and drums. It has sometimes resulted in more flexibility than needed for small diameter cable while it materially improves cable handling somewhat proportionate to the diameter. However, this gain may be effectively traded for larger wire sizes, fewer wires in cable of the same diameter, and lower total sliding friction and internal pressure. It becomes a means of improving other characteristics.

Trade-off improvement, for example, results in longer lay lengths while cable stability inherent in axial symmetry is retained. Ten percent (10%) longer lay lengths have now been used effectively for both strands and cable of standard construction, while on the other hand, the same lay lengths have been held to increase flexibility when the plurality of wires is large and are laid in the same direction in one operation to gain flexibility when stiffness is inherently high. Increased lay length then reduces compressive strength, increases tensile strength, and reduces constructional stretch.

There is an overall object of the invention, it may now be observed, to lower the inertial force levels substantially in the three dynamic modes, and attendantly reduce inertial effects both in terms of balancing fatigue and wear, and damping vibratory characteristics. Subsequent description sets the basis and includes more about the significance of earlier results.

Three (3) assumptions are to be made, one for each of the dynamic modes since it has been noted there are several objects for stress moderation and control, and it is dynamically critical to avoid dominant axial and transverse stresses in elemental planes, and associated compressive stresses and bearing loads. For example, cycle life for s 7 x 19 primary aircraft control cable when using the smallest pulley specified approximates onefifteenth of the life achieved with the largest size pulley specified. The shock environment created by autopilot induced impacts and vibrations clearly contributes to shortened cycle life in all cable/pulley combinations of this system. Critical stress conditions may be overcome in all cases however by simple application of the inertial concept.

First, let it be assumed that a steel cable is under tension (T) within the elastic range, as expressed by t rag/.5

and elastic stretch,

is proportional. This cable with a breaking strength of 30,000 lbs. is then bent around a sheave, when tension (T) is increased :until parts of the wire become plastic. In this dynamic state the bending strain,

will not rise proportionately so that ultimate tension decreases when the cable is static; also surface contact stress will not rise beyond the yield point as a localized stress. Thus the tension required to reach a critical state is essentially that of a straight cable. It is now clear, however, that inertial fatigue is the result of 1) the type of stress, and (2) its magnitude.

Primary load may be reduced normally more than one-half by changing to titanium cable, and thus, the

amount of the weight reduction depends upon the length, and possibly, the amount the length may be shortened. This is a very significant reduction of total weight in deep moorings in terms of stress moderation; on the other hand, in aircraft control cable systems, the total amount of 'weight reduced is minor but the reduction in impact stresses and vibration proves significant in reducing inertial forces for improved control by automatic pilots, and gaining protracted cycle life due to moderated effects upon wear and fatigue; it is also noted by basic weight reduction to aerospace vehicles becomes significant to iiight performance.

Further in the mooring application, let impacts and vibration be considered. If the tension is 25,000 lbs. due to elastic stretch of five ft. it will rise to 50,000l lbs. from a ten ft. stretch, disregarding primary load. Theoretically then this cable breaks when stretch reaches six ft. (6'). During these impacts at the mooring floats or buoys, stress increases according to the formula Ui=VovEpo Then with titanium cable, a five ft. (5') stretch creates a peak of 12,500 lbs., and a ten ft. (10') stretch a peak of 25,000 lbs. so that titanium cable does not fracture and should not overstress.

Vibration of cable, it is recalled, is termed Aeolian dancing in air, and strumming in water, both of which are caused by fluid iiow when cable is under tension. These vibrations are characterized -by short nodal lengths, small amplitude and high frequency so that lengths Since vibration generates low order impacts and flexing, bending fatigue and wear is caused so that weakening develops and fracture ultimately occurs.

Titanium and titanium base alloys are high damping metals. The damping characteristic of titanium wire is found to be improved by workhardening for closer packing of the microstructure, and this characteristic of titanium cable is improved in the seawater temperaof titanium cable is improved in the seawater temperature range. Apparently damping and the critical magnifying effect of vibratory resonance are minimized to result in a further inertial advantage in cable dynamics.

In summary, special inertial advantages of titanium cable in the tension mode are:

(l) Effective use of strength characteristics;

(2) Reduction in cable mass by more than one-half;

(3) Damping of self excited self induced vibration;

(4) Moderation of impacts in shock environments, and

(5 Closely tailored safety factors.

Secondly, let it be assumed that steel cable is in the motion mode, thus it is in tension and bending, as needed to perform work and for handling. Inertial factors added are acceleration, velocity, deceleration, and impacts during starts and stops, starting impacts being especially large due to massive strength inertial forces. In this mode there are the hyperbolic characteristics of inertial loading and the parabolic characteristics of load bending motion with the associated inertial forces of system motion.

Specifically, the hyperbolic condition is a dynamic relationship of two ratios, a stress and elastic ratio (a/E), and a ratio between cable velocity and stress-propagation speed (V0/c). The parabolic relationship consists of the hyperbolic condition as one ratio of the cable (m/m cable). The significant inertial factors are mass, stress, elasticity, and velocity. Longitudinal wave velocity (ft/sec.) is c=\/E/p and transverse wave velocity is e=\/ r/p.

In the motion mode there are added inertial advantages for titanium cable because of lower mass and internal moments of inertia, with velocity, acceleration and deceleration effects producing inertial forces; stress is reduced by one-half approximately (with elasticity also one-half) due to the ratio of tr/E, but this reduction becomes substantially greater when cable cross-section is reduced.

Thirdly, let it be assumed that steel cable is in the drag mode, in tension and motion as before, but drag in viscous mediums is added. This mode changes external forcevector components by adding external forces which increases line tension and the severity of vibration. In turn, inertial effects of fatigue and wear are increased. Added factors are a drag force and a related Reynolds number,

inertial f oroe viscous force Cable diameter and vibration are, of course, critical parameters in this mode, so that it may be expected that intertial forces of titanium cable would be reduced to approximately one-quarter after reducing diameter.

In summary innovations of active and passive parts of the inertial concept add to achieving higher performance in drag, to substantially reducing stresses, to damping vibration and by linear transformation to uncoupled systems, to moderating acoustical, aerodynamic, and hydrodynamic effects.

Dynamic conditions in the three modes are also found to apply to composite cable because of parallel electrical core development so that equivalent advances may be expected from integrating electrical and mechanical cornponents within this concept. Load deflection diagrams of inertially suitable contra-helical composite cable developed for helicopter cargo handling are described in outline:

(a) Contra-helically wrapped Fyle" 1 x 42 conventional galvanized and copper conductor core fractured at 7600 lbs. but began overstressing at 4200 lbs. under load deflection.

(b) Contra-helically wrapped 1A" 1 x 30 high-strength Ti-13V-11Cr-3Al wires, with a specially designed electrical core, fractured at 7200 lbs. but did not overstress until it reached 5200 lbs. The special core did not fail under deflection load or within the cycle life period of the cable. Additional breaking strength would have been obtained if the inner wrap lay length had been longer as indicated in distinctly curvalinear loading deflection.

(c) Contra-helically wrapped, 5/16" 1 X 30 medium strength Ti-6Al-4V cable with special core achieved 91% linearity and 85% efficiency, to overstress at 5500 lbs. and fracture at 6150 lbs. Again the core did not fail in load deflection or within the cycle life period of the specimen. This diagram showed a remarkable degree of linearity.

Inertial force level is clearly lowered. However, mathematical formulation depends upon kinematic and geometric constraints and physical laws governing behavior of the system. Motion of a single point mass obeys according to Newtons second law of motion, and expressed as the first derivative becomes QL afm etz as a partial differential equation. Displacement from equilibrium u results in strain lll and by Hookes law Special techniques for embodying the inertial concept may now be appropriately used as herewith described in high performance applications.

First- A two step process for reducing mass and minimizing diameter is effective as outlined:

(l) Substitute titanium test lengths of the same size and construction for steel cable so that both cables are compared by load deflection diagrams for limiting loading and energy absorption, and if practicable, perform cycle tests for determining hyperbolic and parabolic conditions. The first step is completed by determining the strength level to which the new titanium cable may be reduced, level of impact stresses, and the dynamic factor of safety.

(2) In the second step change design for the specific application by the following inputs, i.e. change construction by reducing diameter and number of wires, increase lay lengths over steel construction by approximately ten percent and use core wires of greater elasticity, to also gain in efiiciency.

These changes will substantially improve both active and passive characteristics, but because of their extent, it may prove desirable to proceed with further optimization.

Secondly.-Linearity is determined, preliminarily for loading by taking a load deflection diagram, followed by two sets of cycle tests. The first set is to determine the hyperbolic condition of the design to be used by testing not less than four loading levels with at least two in the knee of the curve. It may also be plotted by developing two ratios, r/E and I/O/c, having obtained E from the load deflection diagram and c from the ratio, \/E/p.

The second set is to determine the parabolic condition of the cable at about the same number of D/a ratios, obtaining three plots, essentially linear, beyond the knee of the curve.

A series of curves may then be plotted with the data available to show limits of linearity and the increase in cycle life achieved by use of approximately linear dynamic conditions. Bend stresses are found to moderate at lower D/ d ratios in titanium cable compared to steel.

(3) Core size and accordingly core function is increased in each dynamic mode, and as feasible, cores only are used in the tension mode. This technique is effective when the core will sustain the full primary load and as much as feasible of the inertial and impact loads. In so doing severe stress raisers at cross points may be generally avoided first by simplifying construction and next by controlling lay directions. In other cases techniques may be used to spread bearing loads such as lightly swaging layer interfaces and applying solid film.

The kinetics of combining stresses at interfaces of contrahelical construction and cross over points of axially symmetric cable creates severe stress raisers and loss of efficiency in the interchange of energy so that cycle life is lost.

The use of more elastic core wires also prevents overstressing these wires as frequently occurs at high loads or impacts in service.

Thus supporting techniques may be used to increase stratified dynamics between core and outer strand components to further reduce fatigue and wear.

(4) Stratification of stresses is directly related to increasing core size and function so that it largely results as a by-product of core improvement in that core elasticity is increased, construction is simplified, lay lengths are increased, and stress raisers are reduced by improving bearing surfaces and decreasing the number of crossover points.

Finally these contributions to stratification each reduce constructional action so that equivalent to elastic string action is approached.

This technique then reduces low order impacts and contributes resistance to fatigue and wear in all shock environments.

(5) The uniquely passive property of corrosive inertness is the key to the second part of the inertial concept so that degradation is essentially confined to the dynamic aspects of fatigue and wear which would include damping for a number of applications.

Protracted cycle life is further assured through the practical balance achieved between Wear and fatigue by use of long wear life solid film lubricant. Again, undisturbed oxide surfaces of titanium wire results in a low coefiicient of sliding friction in the used environments. It is already noted that no wear occurred in one-million cycles, whereas at the opposite extreme with no lubrication under loading, wear was normally progressive to a remaining one-half the wire diameters when fractures began to occur. Therefore with cable in motion cycle life may now be seen to be a function of lubrication very much the same as other dynamic mechanism with equivalent effects upon cycle life.

(6) Dancing and strumming are in fact a fatigue effect not yet under control although titanium has a high damping index. It has also been discovered that Workhardening, and sometimes sea water temperatures, improve the damping characteristic. Further investigation is to be undertaken of the oceanographic cable now being fabricated using tension and fluid pressure as the two principal parameters. Anti-vibrational masses are to be considered.

Stress control and moderation embodied in both parts of the inertial concept may now be summarized:

(a) Substantial reduction of mass in cables to perform work is achieved so as to moderate the elementary and compressive stresses, a major consideration in multipart reeving and long cable systems.

(b) Tension is moderated to the extent that mass and inertial loading are reduced, a major consideration in a number of systems.

(c) Bend stresses are substantially reduced, a major consideration in motion and drag systems.

(d) Impact stresses are halved, a major consideration in long tension members and in shock environments.

(e) Construction is simplified and lay lengths increased to increase efficiency, reduce stresses and increase strength.

(f) Core functions may be increased to increase performance, reduce stresses, and prevent core overstressing.

(g) Stress stratification improves performance and efficiency while reducing stress-raisers, wear and fatigue.

(h) Constructional stretch action is largely eliminated to reduce impacts, fatigue and wear.

(i) Wear and fatigue effects are in practical balance at least in a substantial range of cable dynamics to control severe wear as well as reduce fatigue.

(j) Vibration may be found to have a degrading inertial effect, but more limited in titanium cable than commonly used materials because of a high damping index and reduced stresses and forces.

(k) Corrosive inertness confines degradation to wear and fatigue, and the uncertain effects of vibration in this concept.

It will now be understood new cable technology surrounding the inertial concept requires the use of cable principles, which in turn, involves development of suitable processing, fabrication equipment and testing that will cumulatively result in novel features for production cable.

Novel cable principles used in this inertial concept are:

(1) Embodiment of active Well defined inertial characteristics, moderated by lower internal moments of inertia, as a novel principle, to efficiently perform work for the purpose of augmenting or replacing completely the dominantly massive strength approach to cable dynamics generally used.

(2) Embodiment of passive well defined, moderated characteristics, combined by novel techniques, to sustain inertial effects for protracted service in normal environments including aerospace and hydrospace for which temporizing techniques are currently used.

(3) Fully embody performance characteristics required for an application, including high performance, primarily based upon the mode of the dynamic state of the system, and secondarily upon wire, strand and cable design requirements to sustain characteristic dynamics inherent in the application at level performance.

(4) Use of a dynamic safety factor based upon (l) specied inertial force or work levels for protracted performance, and (2) effectiveness of control exercised over cable dynamics; the basis of this principle is performance characteristics integrated with safety. High impact tolerance permits the use of a 10W dynamic factor of safety.

(5) Use of an inertial performance and reliability factor based upon (1) proctracted level performance due to passive inertness, and (2) control of fatigue and wear.

(6) Use of cycle life design factors for establishing linear cable performance in the motion and bending modes.

(7) Use of cores with increased functions, and relatedly, the stratification of stresses.

(8) Combination of techniques to achieve moderated stress and pressure control in dynamic states of tension, motion, and drag to substantially improve performance characteristics.

(9) Embody inertial characteristics fully to minimize cable diameter so as to increase handling and operating rates, and also minimize viscous drag, vibratory and acoustical effects.

(10) Interdependent control of inertial characteristics of tow cable in the drag mode and linear transformation of coupled aerodynamic, hydrodynamics and acoustical effects to substantially improve system performance characteristics.

(11) Use of formal methodology for synthesizing and optimizing inertial gains of high performance systems resulting from property values developed in wire fabrication, new cable technology used in design, processing and testing, and production results.

These novel principles are indicative of the broad technological base supporting the inertial concept, and are outlined as basis =for claims herewith,

I claim:

1. An elastic cable having more than forty percent (40%) of the constructional stretch removed with less stiffness and greater springback, having a plurality of ductile titanium alloy wires and being a long tension member.

2. An elastic cable having more than forty percent (40%) of the constructional stretch removed 'with less stiffness and greater springbaok, having a plurality of corrosively resistant, ductile titanium alloy wires, and being a long tension member whereby hoisting and Work capacity is high, handling is rapid, and cable rotation is low.

3. An elastic cable having more than forty percent (40%) of the constructional stretch removed with less stiffness and greater springback, having a small diameter from the plurality of ductile titanium alloys wires, and being a long tension member is dominant in energy absorption and damping whereby it is suitable for aircraft control cable and oceanographic cable.

4. An elastic cable having more than forty percent (40%) of the constructional stretch removed with less stiffness, greater springback and high damping, having a plurality of ductile, corrosively resistant titanium alloy wires coated with long wear life solid lm, and being a long tension member whereby wear is neutralized and maintenance limited, performance is level and reliable, tension and tension peaks with viscous drag are low.

References Cited UNITED STATES PATENTS 2,974,076 2/ 1961 Vordahl 14S-12.7 3,156,590 11/1964 Vordahl 148-12.7 3,169,085 2/1965 Newman. 3,340,051 9/1967 Evans et al 75-175.5 3,271,944 9/ 1966 Stevens 57-145 3,343,951 9/1967 Peebles 75-175.5 3,364,017 l/l968 Day -175.5 3,368,881 2/1968 Abkowitz et al 75-175.5 3,394,036 7/ 1968 Parris.

DONALD E. WATKINS, Primary Examiner US. C1. AXR? 148-415 

